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We construct confidence sets for the regression function in nonparametric binary regression with an unknown design density. These confidence sets are adaptive in $L^2$ loss over a continuous class of Sobolev type spaces. Adaptation holds in…

Statistics Theory · Mathematics 2016-08-04 Rajarshi Mukherjee , Subhabrata Sen

Numerous recent works show that overparameterization implicitly reduces variance for min-norm interpolators and max-margin classifiers. These findings suggest that ridge regularization has vanishing benefits in high dimensions. We challenge…

Machine Learning · Statistics 2021-12-20 Konstantin Donhauser , Alexandru Ţifrea , Michael Aerni , Reinhard Heckel , Fanny Yang

Good generalization performance on high-dimensional data crucially hinges on a simple structure of the ground truth and a corresponding strong inductive bias of the estimator. Even though this intuition is valid for regularized models, in…

Machine Learning · Statistics 2022-10-28 Konstantin Donhauser , Nicolo Ruggeri , Stefan Stojanovic , Fanny Yang

Higher-order regularization problem formulations are popular frameworks used in machine learning, inverse problems and image/signal processing. In this paper, we consider the computational problem of finding the minimizer of the Sobolev…

Numerical Analysis · Mathematics 2023-10-20 Adrien Weihs , Jalal Fadili , Matthew Thorpe

Neural networks trained by gradient descent (GD) have exhibited a number of surprising generalization behaviors. First, they can achieve a perfect fit to noisy training data and still generalize near-optimally, showing that overfitting can…

Machine Learning · Computer Science 2023-10-05 Zhiwei Xu , Yutong Wang , Spencer Frei , Gal Vardi , Wei Hu

It is well-known that a deep neural network has a strong fitting capability and can easily achieve a low training error even with randomly assigned class labels. When the number of training samples is small, or the class labels are noisy,…

Computer Vision and Pattern Recognition · Computer Science 2024-09-10 Avraham Chapman , Lingqiao Liu

We show that label noise exists in adversarial training. Such label noise is due to the mismatch between the true label distribution of adversarial examples and the label inherited from clean examples - the true label distribution is…

Machine Learning · Computer Science 2023-10-17 Chengyu Dong , Liyuan Liu , Jingbo Shang

Motivated by surprisingly good generalization properties of learned deep neural networks in overparameterized scenarios and by the related double descent phenomenon, this paper analyzes the relation between smoothness and low generalization…

Machine Learning · Computer Science 2021-10-29 Yuege Xie , Hung-Hsu Chou , Holger Rauhut , Rachel Ward

The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually…

Statistics Theory · Mathematics 2013-12-19 Raymond J. Carroll , Aurore Delaigle , Peter Hall

Overparameterized neural networks (NNs) are observed to generalize well even when trained to perfectly fit noisy data. This phenomenon motivated a large body of work on "benign overfitting", where interpolating predictors achieve…

Machine Learning · Computer Science 2024-03-22 Guy Kornowski , Gilad Yehudai , Ohad Shamir

Overfitting and generalization is an important concept in Machine Learning as only models that generalize are interesting for general applications. Yet some students have trouble learning this important concept through lectures and…

Machine Learning · Computer Science 2022-09-08 Matias Valdenegro-Toro , Matthia Sabatelli

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…

Numerical Analysis · Mathematics 2017-10-13 Ernesto De Vito , Massimo Fornasier , Valeriya Naumova

We study overparameterization in generative adversarial networks (GANs) that can interpolate the training data. We show that overparameterization can improve generalization performance and accelerate the training process. We study the…

Machine Learning · Computer Science 2024-05-02 Lorenzo Luzi , Yehuda Dar , Richard Baraniuk

In this paper we propose a unified approach, based on limiting interpolation, to investigate the embeddings for the Sobolev space $(\dot{W}^k_p(\mathcal{X}))_0, \, \mathcal{X} \in \{\mathbb{R}^d, \mathbb{T}^d, \Omega\}$, in the subcritical…

Functional Analysis · Mathematics 2020-10-23 Oscar Domínguez , Sergey Tikhonov

Meta learning has demonstrated tremendous success in few-shot learning with limited supervised data. In those settings, the meta model is usually overparameterized. While the conventional statistical learning theory suggests that…

Machine Learning · Computer Science 2022-11-10 Lisha Chen , Songtao Lu , Tianyi Chen

It has been hypothesized that label smoothing can reduce overfitting and improve generalization, and current empirical evidence seems to corroborate these effects. However, there is a lack of mathematical understanding of when and why such…

Machine Learning · Computer Science 2020-10-27 Blair Chen , Liu Ziyin , Zihao Wang , Paul Pu Liang

Mislabeled samples are ubiquitous in real-world datasets as rule-based or expert labeling is usually based on incorrect assumptions or subject to biased opinions. Neural networks can "memorize" these mislabeled samples and, as a result,…

Machine Learning · Computer Science 2021-11-24 Katharina Rombach , Gabriel Michau , Olga Fink

This paper analyzes the generalization error of minimum-norm interpolating solutions in linear regression using spiked covariance data models. The paper characterizes how varying spike strengths and target-spike alignments can affect risk,…

Machine Learning · Statistics 2025-10-03 Jiping Li , Rishi Sonthalia

The reason for Meta Overfitting can be attributed to two factors: Mutual Non-exclusivity and the Lack of diversity, consequent to which a single global function can fit the support set data of all the meta-training tasks and fail to…

Machine Learning · Computer Science 2024-11-12 Manas Gogoi , Sambhavi Tiwari , Shekhar Verma

Overfitting in deep learning has been the focus of a number of recent works, yet its exact impact on the behavior of neural networks is not well understood. This study analyzes overfitting by examining how the distribution of logits alters…

Machine Learning · Computer Science 2019-10-02 Zeju Li , Konstantinos Kamnitsas , Ben Glocker